An implicit meshless scheme for the solution of transient non-linear Poisson-type equations |
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Authors: | G.C. Bourantas V.N. Burganos |
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Affiliation: | 1. Applied Mathematics and Computational Science and Earth and Environmental Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;2. Institute of Chemical Engineering Sciences—Foundation for Research and Technology, Stadiou, Platani, Patras 26504, Greece |
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Abstract: | A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. |
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Keywords: | Meshfree point collocation method MLS Nonlinear Poisson equation Linearization method Lagging coefficients |
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